We consider critical branching Brownian motion with absorption, in which there is initially a single particle at x>0, particles move according to independent one-dimensional Brownian motions with the critical drift of -2, and particles are absorbed when they reach zero. Here we obtain asymptotic results concerning the behavior of the process before the extinction time, as the position x of the initial particle tends to infinity. We estimate the number of particles in the system at a given time and the position of the right-most particle. We also obtain asymptotic results for the configuration of particles at a typical time.